French President Francois Hollande said almost 30,000 people have died and asked: "How many more deaths will we wait for before we act? How can we let the paralysis of the United Nations to continue?"
"I know one thing is certain, the Syrian regime will never again take its place in the council of nations. It has no future among us," he said.
He called on the United Nations to protect "liberated zones" within Syria and to ensure humanitarian aid to refugees.
Ban also expressed profound concern at continuing violence in Afghanistan and Congo, increasing unrest across west Africa's Sahel region where al-Qaida has made inroads, and the "dangerous impasse" between Israelis and Palestinians that may close the door on the two-state solution.
The "shrill war talk" by Israel in recent weeks, in response to its belief that Iran is pursuing nuclear weapons, "has been alarming," Ban said, and Tehran's rhetoric threatening Israel's existence is unacceptable.
"Any such attacks would be devastating," he said, reminding the presidents, prime ministers, monarchs and diplomats from the 193 U.N. member states of the need for peaceful solutions and respect for international law.
"Leaders have a responsibility to use their voices to lower tensions instead of raising the temperature and volatility of the moment," he said.